Bunuel wrote:
If a wire is bent into the shape of a square, then the area enclosed by the square is 81 cm square. When the same wire is bent into semi-circle. then the area of semi circle will be
A. 22 cm square
B. 44 cm square
C. 77 cm square
D. 81 cm square
E. 154 cm square
Since the area of the square is 81, the side is 9, and thus the perimeter is 36. Since 36 is the perimeter of the semicircle, we know that, in terms of the circle’s radius, the semicircle’s perimeter is twice the radius and half the circumference (of the entire circle). Thus, we can create the following equation in which r = radius:
2r + 2πr/2 = 36
2r + πr = 36
r(2 + π) = 36
r = 36/(2 + π)
Since π is slightly greater than 3, r is approximately 36 divided by a number slightly greater than 5. So we can approximate r as 7. Using this approximation, we calculate the area of the semicircle as:
1/2 x π x 7^2
1/2 x π x 49
If we round π down to 3 and 49 up to 50, we have:
1/2 x 3 x 50 = 75
So the area of the semicircle is approximately 75 square cm. We see that choice C must be the correct answer.
Answer: C
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